There is no single conversion--that's the whole point of using a scale. For example, flour will vary in "density" (i.e. grams per cup) depending on humidity, type of flour, whether you sift it or not, how tightly you pack the measuring cup, etc. That is why it's more accurate to use weight, rather than volume, for solid measurements. The problem is that many recipes don't give weights, just volumes, though more baking recipes these days do give weight measures recognizing their greater accuracy.

Having said that, a quick Google search will give you many rough conversions. See for example
volume to weigh conversion tables

clinresga nailed it. Mass-Volume calculations will vary depending on the item. You cant account of environmentals but The link I list below allows to to select the product.

Here is a link that might be useful: Food Product Calculation Tools

one o the reasons for the differences is that austrailians are as stupid as americans and they have their own system :) but unlike ours, they use the same terms but mean different amounts. you always have to check the location of your conversion tool :)